What is the solution for y^{''}+16y=3e^{8x} ?

The solution for y^{''}+16y=3e^{8x} is y=c_{1}cos(4x)+c_{2}sin(4x)+3/80 e^{8x}

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y^{''}+16y=3e^{8x}

y^{^{''}} + 16 y = 3 e^{8 x}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{3}{80} e^{8 x}

Solution steps

y^{''} (x) + 16 y = 3 e^{8 x}

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{3}{80} e^{8 x}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{3}{80} e^{8 x}

y^{^{''}} + y^{^{'}} - 2 y = sin (2 x)

4 y^{^{''}} + 2 y = 4 x^{3} + 5 x^{2} - x + 7

y^{^{''}} - 3 y^{^{'}} + 2 y = cos (x), y^{^{'}} (0) = 2, y (0) = 0

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = 2 x^{2} + 4 sin (x)

y^{^{'''}} - 12 y^{^{''}} + 48 y^{^{'}} - 64 y = 4 e^{4 x}

What is the solution for y^{''}+16y=3e^{8x} ?
The solution for y^{''}+16y=3e^{8x} is y=c_{1}cos(4x)+c_{2}sin(4x)+3/80 e^{8x}